SWEDEN

Abstract

Breast cancer is diagnosed in more than 6300 Swedish women every year. Mammograms,

which are X-ray images of breasts, are taken as part of a nationwide screening process and are analyzed for anomalies by radiologists. This analysis process could be made more eﬃcient by using computer-aided image analysis to assist quality control of the mammograms.

However, the development of such image analysis methods requires what is called a “ground truth”. The ground truth is used as a key in algorithm development and represents the true information in the depicted object. Mammograms are 2D projections of deformed 3D objects, and in these cases the ground truth is almost impossible to procure. Instead a surrogate ground truth is constructed.

ALGSII, a novel method for ranking shapes within a given set, was recently developed for measuring the level of agreement among ensembles of markings produced by experts of glandular tissue in mammograms. It was hypothesized in this thesis that the ALGSII measure could be used to construct a surrogate truth based on the markings from domain experts.

Markings from segmentations of glandular tissue, performed by 5 diﬀerent ﬁeld experts on 162 mammograms, comprised the working data for this thesis project. An algorithm was developed that, given a ﬁxed set of markings, takes an initial shape and modiﬁes it iteratively until it becomes the “optimal shape” - the shape with the highest level of agreement in the group of markings according to the ALGSII measure. The algorithm was optimized with regard to rate of accepted shape changes and computational complexity.

The developed algorithm was successful in producing an optimal shape according to the deﬁnition of maximizing the ALGSII measure in 100% of the cases tested. The algorithm showed stability for the given data set, and its performance was signiﬁcantly increased by the implemented optimizations.

ii Acknowledgements I wish to thank my supervisors, Dr. Christina Igasto1 and Dr. Fredrik Georgsson, my fellow students for much good advice, and not least, my partner Jennifer Frankel who inspired and helped me to ﬁnish this thesis.

1 During the major part of this thesis project her last name was Ols´n e iii iv Contents

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2.1 An ensemble of expert markings of glandular tissue performed on the same X ray......................................... 7

2.2 An α value is calculated for each member of the ensemble, shown in Figure 2.1, in relation to the rest of the ensemble on a leave-one-out-basis. In each subﬁgure the top left ﬁgure represents the computation of MB from equation (2.8) and the top right ﬁgure represents the computation of DB from equation (2.6). The two lower ﬁgures represents how the set S(Ai − A5 ) maximizes (to the right) MB (Ai ) and minimizes (to the left) DB (Ai )............. 9

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4.2 The α values for all experts and the optimized shape during the course of optimization for case 199.............................. 22

4.3 The lines represent the cumulative sum of accepted changes at a given number of iterations..................................... 24 4.4 (a) to (e) show each expert’s segmentation. (f) shows all expert segmentations superimposed into one image to illustrate the agreement between them. (g) is the optimized shape constructed using the aforementioned algorithm. In (h), (g) has been added to f for comparison.................... 25 4.5 (a) to (p) show how the intermediate shape Sb changes as it approaches the optimal shape S ∗. (a) is the initial guess derived as described in section 3.6.. 26 4.6 (a) to (e) show each expert’s segmentation. (g) shows all expert segmentations superimposed into one image to illustrate the agreement between them. (h) is the optimized shape constructed using the aforementioned algorithm. In (i), (g) has been added to (h) for comparison................... 26 4.7 (a) to (p) show how the intermediate shape Sb changes as it approaches the optimal shape S ∗. (a) is the initial guess derived as described in section 3.6.. 27 Chapter 1 Introduction

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In Sweden each year more than 63001 new cases of breast cancer are diagnosed in women, and about 1500 women die from the disease [1]. This makes breast cancer the most common type of cancer aﬀecting Swedish women. As a preventative measure, the Swedish National Board of Health and Welfare has issued a recommendation to the Swedish county councils to oﬀer women recurring screenings. The screening process consists of taking X-ray images of the breasts. These X rays, called mammograms, are then analyzed by a radiologist for anomalies. The National Board of Health and Welfare recommends the county councils to call every woman between the age of 40 and 50 for screening every 18 months, and every woman between the age of 51 and 74 every 2 years [2]. This screening program helps detect cancer at an early stage when treatablilty is high. Women who are screened regularly show a decreased mortality of about 30% [3].

The radiologist’s tasks are to verify the quality of the image to determine if it needs to be retaken, and, if the image passes quality scrutiny, to determine a diagnosis. It has also been shown [4] that letting more than one expert assess each mammography image significantly increases the chance of a correct diagnosis. With regard to the quality assessment of mammograms, a study by Basset et. al. [5] showed that 44% of mammograms needed to be retaken due to insuﬃcient quality. Evidently there is room for improvement on both quality assessment and diagnostic analysis.

Computer aided image analysis could aid in the process of analyzing the mammograms and serve as a second opinion. This has two main beneﬁts. As opposed to the intra- and inter-expert ﬂuctuations in radiologist assessments it will be consistent in the sense that given the same input it will always produce the same output. Also, computer aided image analysis could be used to rapidly perform quality checks, and thus make the screening process more eﬃcient. Maintaining a high quality in the mammographic imaging process is vital as each unusable X ray will have subjected the patient to unnecessary, and by itself carcinogenic, radiation.

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1.2 The problem of ﬁnding a ground truth When solving image analysis problems the goal is to replace a diﬃcult or tedious process with an automated one. The development of such an automated process requires providing feedback to the process algorithm on how to diﬀerentiate diﬀerent cases and to show what is a correct output and what is not. Consider the following example: A ﬁsh packaging factory has decided to use an image analysis solution for counting the number of ﬁsh that pass through the factory each day. They start with a preliminary algorithm, and to tweak the performance of the algorithm they need to know when the algorithm produces the correct output. To verify the correctness of the algorithm used, they simply stop the ﬁsh conveyor belt and compare the actual ﬁsh count to the number generated by the algorithm. This feedback process allows the engineers to adapt the algorithm during a training phase using what is called ground truth 2, i.e., the actual value of the observed event. In this case the ground truth is the actual number of ﬁsh on the conveyor belt.

The concept of ground truth is crucial for measuring performance in image analysis.

Without it, it cannot be determined wether or not the goal has been reached. Nor is there any way of assessing whether an alteration to the algorithm has improved it or made it worse.

In many cases the ground truth is readily available as in the above example. However, there are some situations where the ground truth is not easily accessible or simply unknown. This is particularly evident in medical imaging where you often have only 2D representations, such as X rays, of 3D objects, and invasive surgery to verify the correctness of your algorithm is not feasible.

When analyzing mammographic images in the breast cancer screening process, one of the radiologist’s tasks is to identify the portion of the image which represents glandular 2 Theterm “ground truth” stems from the ﬁeld of cartography where it means ‘the truth on the ground’ or ‘on location’.

tissue. Figure 1.1 shows glandular tissue marked on an X ray of a breast. In the interest of developing an automated process that could perform this segmentation of glandular tissue from fatty tissue, a ground truth would be necessary to have something to train the algorithm with. The closest thing to a ground truth in this case is a domain expert assessment. Letting a radiologist, the domain expert in this case, manually trace the boundary of the glandular tissue in a mammogram gives an approximation of the ground truth, a surrogate ground truth.

Figure 1.2 shows an example of expert markings of glandular tissue in the same mammogram.

Note how diﬀerently the diﬀerent experts assessed the same X-ray image. It is likely that combining the diﬀerent expert markings into one image would yield a better approximation of the underlying ground truth than any single expert marking. This combined marking would then represent the surrogate ground truth.

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Figure 1.2: The glandular tissue as outlined by ﬁve radiologist assessing the same X-ray image.

1.3 Thesis objective In [6] Ols´n and Georgsson proposed a method, ALGSII, to estimate the level of agreement e among an ensemble of markings produced by domain experts. The method ranks the experts’ markings within the ensemble. It was hypothesized that this method could be used to ﬁnd an unknown optimal shape that maximizes the ALGSII-metric. This shape, having the highest level of agreement with all the included expert markings, would represent the best approximation of the underlying ground truth, given the knowledge of the experts.

The goal of this thesis was to develop a method that, given an ensemble of markings produced by experts, ﬁnd a shape which maximizes the ALGSII-measure. This shape would be seen as the best possible approximation of the underlying ground truth regarding segmentation of glandular tissue versus non-glandular tissue in a mammogram, as based on the expertise of the radiologists.

4 Chapter 1. Introduction Chapter 2 Background This chapter introduces the reader to technical concepts and previous research relevant to this thesis. In particular the ALGSII-method is described.

Binary image is an image represented as an array of values where the only allowed value for a pixel is 1 or 0. This is equivalent to saying that the image has a bit depth of 1, i.e., one bit is necessary to store the value of one pixel. [7] Image topology is deﬁned as the properties of an image which are not aﬀected by any deformation. This would be, e.g., the number of connected areas, or the number of holes in a binary image [7].

Morphological operations are modifying operations on images based in set theory. Examples of morphological operations are union, intersection, dilation, erosion, etc. [7].

Structuring element is often used as a reference to the smaller of two sets in a morphological operation between two sets [7].

Dilation is a morphological operation used to increase the size of a shape [7]. Dilation is denoted by ⊕, and for the set A and a structuring element B in Z2 dilation is deﬁned as

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